Location-based Propagation Modeling for Opportunistic Spectrum Access in Wireless Networks

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science at George Mason University

By

Tugba Erpek Bachelor of Science

Osmangazi University, 2005

Director: Brian L. Mark, Associate Professor Department of Electrical and Computer Engineering

Fall Semester 2007 George Mason University

Fairfax, VA

Copyright © 2007 by Tugba Erpek All Rights Reserved

ii

DEDICATION

To my parents, brother Can, sister Esra, and roommates Burcu and Astrid for all their support…

iii

ACKNOWLEDGEMENTS

I would like to thank Dr. Mark for all his guidance during my graduate study. I always felt the privilege of having a supportive and encouraging professor throughout the two years I worked with him.

Thanks to my committee members, Dr. Wage and Dr. Nelson for always being

kind to spare their valuable time to give feedback on my work. Thanks to Ahmed Nasif for all his help and feedback on my thesis. Thanks to Mark McHenry, Karl Steadman and Alexe Leu from Shared Spectrum

Company for their helpful discussions and comments. Thanks to my family for all their support during my study. This work was supported by the U.S. National Science Foundation under Grant

No. CCR-0209049 and Grant No. ECS-0426925.

iv

TABLE OF CONTENTS

Page List of Tables…….........................................................................……...........................vi List of Figures...............................................................................…….......................... vii Abstract.................................................................................................................……..viii 1. Introduction.............................................................................................................…1 2. Propagation Models ....................................................................................................4

2.1 Empirical Propagation Model (EPM)-73 .............................................................4 2.2 Okumura-Hata Model ...........................................................................................5 2.3 Longley-Rice Model .............................................................................................6 2.4 Tirem Model .........................................................................................................6

3. Location-Based Propagation Model ...........................................................................8 3.1 Tiling Algorithm .................................................................................................10

4. Application of LPM to Opportunistic Spectrum Access ..........................................28 4.1 Determining the Percentile of Loss for a Given Transmitter and Receiver........28 4.2 Using LPM to Determine MIFTP.......................................................................34

5. Performance Evaluation of LPM ..............................................................................36 5.1 Memory Requirement .........................................................................................36 5.2 Violation Probability...........................................................................................37 5.3 Calculation Time.................................................................................................38

6. Spectrum Sensing via the Multitaper Method ..........................................................41 6.1 Spectral Estimation .............................................................................................42 6.1.1 Conventional FFT Method.........................................................................42 6.1.2 Multitaper Method .....................................................................................43 6.2 Numerical Results...............................................................................................45

7. Conclusion ................................................................................................................54 Bibliography ...................................................................................................................57

v

LIST OF TABLES

Table Page Table 4.1.1 Grouping Distances into Distance Bins..…………………………………30

vi

LIST OF FIGURES

Figure Page Figure 3.1 Interference Caused to the Legacy User Receiver ........................................................................9 Figure 3.1.1 Terrain Profile ..........................................................................................................................11 Figure 3.1.2 Non-parametric pdf of Losses for the Whole Region ..............................................................11 Figure 3.1.3 Whole Region Divided into Sub-areas.....................................................................................12 Figure 3.1.4 Non-parametric pdf of Losses for Sub-areas............................................................................13 Figure 3.1.5 Whole Region Divided into Quadrants ....................................................................................14 Figure 3.1.6 Non-parametric pdf of Losses for Quadrants ...........................................................................14 Figure 3.1.7 Initial Seed ...............................................................................................................................17 Figure 3.1.8 First Percentile of Loss Distribution for the Initial Seed..........................................................17 Figure 3.1.9 Diagonal Increase of the Seed Size ..........................................................................................18 Figure 3.1.10 Diagonal Binary Search – Mean Seed Length is Found.........................................................19 Figure 3.1.11 Diagonal Binary Search – Check the Difference Between L and Lo ......................................20 Figure 3.1.12 Diagonal Binary Search – Continue if the Initial Criteria is not Satisfied .............................20 Figure 3.1.13 Diagonal Binary Search – Optimum Seed Size is Determined Diagonally............................21 Figure 3.1.14 Horizontal Growth .................................................................................................................22 Figure 3.1.15 Horizontal Binary Search.......................................................................................................23 Figure 3.1.16 Vertical Growth......................................................................................................................24Figure 3.1.17 Vertical Binary Search ...........................................................................................................25 Figure 3.1.18 Tiled Region...........................................................................................................................26 Figure 3.1.19 Tiled Region with Overlapping Sub-areas .............................................................................27Figure 4.1.1 Numbered Tiles........................................................................................................................28 Figure 4.1.2 Transmitter and Receiver Pair in the Same Tile.......................................................................31 Figure 4.1.3 Transmitter and Receiver Pair in Different Tiles .....................................................................33 Figure 5.3.1 A Given Transmitter and Receiver Far Away From Each Other .............................................39 Figure 5.3.2 A Given Transmitter and Receiver Close to Each Other .........................................................39 Figure 6.2.1 Max-Hold Plot for TV Channel 3 Using the FFT Method.......................................................46 Figure 6.2.2 Max-Hold Plot for TV Channel 3 Using the MT Method........................................................46 Figure 6.2.3 Number of correctly identified busy channels vs. Threshold Value ........................................50 Figure 6.2.4 Number of False Alarm Channels vs. Threshold Value...........................................................51 Figure 6.2.5 Number of Miss-Detected Channels vs. Threshold Value .......................................................52 Figure 6.2.6 Number of Correctly Identified Free Channels vs. Threshold Value.......................................53

vii

ABSTRACT LOCATION-BASED PROPAGATION MODELING FOR OPPORTUNISTIC SPECTRUM ACCESS IN WIRELESS NETWORKS Tugba Erpek, M.S. George Mason University, 2007 Thesis Director: Dr. Brian L. Mark

Wireless spectrum has become a scarce resource due to the exponential growth of

the number and type of devices that utilize the electromagnetic spectrum. The cost of

long term leasing of spectrum has proven to be a major road block in efficient use of

frequency spectrum. Moreover, spectrum measurement studies have shown that

substantial portions of the allocated wireless spectrum are highly underutilized. Thus,

Dynamic Spectrum Access (DSA) devices have been proposed to be allowed to share the

spectrum dynamically between users. The idea is that the DSA devices will continuously

scan the spectrum and start to transmit in a channel when a licensed user’s operation is

not detected in that channel. Detailed path loss models are needed to calculate the

propagation loss between a DSA device transmitter and a licensed user receiver in order

for the DSA device to avoid causing interference to the receiver by using overly high

transmit power levels.

This thesis proposes a novel propagation loss model called Location Based

Propagation Modeling (LPM) based on the existing TIREM path loss model. The TIREM

model gives the median value of the path loss for a given transmitter and receiver pair

and the user needs to know the precise locations of the transmitter and receiver to

calculate the path loss with the TIREM model. However, for DSA applications, we

usually do not know the precise locations of the licensed user receivers. Furthermore,

TIREM model requires detailed terrain information stored in the memory to calculate

path loss, but DSA devices have limited memory. As a result, we need a compact

representation of the TIREM model which gives the path loss without the need to store

terrain information in the memory. These were the motivations to develop the LPM.

DSA devices require accurate spectral estimation methods to determine whether a

channel is occupied in a specific time and location. Two spectral estimation methods:

multitaper spectral estimation method and conventional FFT-based spectral estimation

method are compared in this thesis using real signal measurements. Our numerical results

show that the multitaper approach yields a significant increase in the number of harvested

channels, while maintaining a smaller probability of false alarm.

Chapter 1: Introduction

The electromagnetic radio spectrum is a natural resource and the use of

transmitters and receivers is licensed by governments [1]. Currently, wireless spectrum is

partitioned into fixed frequency bands by the Federal Communications Commission

(FCC). Over the last decade, it has become a highly valued resource due to the

exponential growth of the wireless communications industry. Moreover, spectrum

measurement studies have shown that substantial portions of the allocated wireless

spectrum are highly underutilized [2]. As a result, the approach of partitioning the

spectrum into fixed frequency bands causes a waste of wireless resources.

Dynamic Spectrum Access (DSA) is a promising approach to increase the

efficiency of the spectrum usage. This approach allows unlicensed wireless users to

access the licensed bands from the legacy spectrum holders on an opportunistic basis [3].

The idea is that the DSA devices will continuously scan the frequency spectrum and start

to transmit in a channel when the licensed users do not transmit at that frequency.

Furthermore, DSA devices will abandon the channel that they transmit within a certain

time when they sense the legacy user’s activity on the same channel again. DSA

technology makes use of various capabilities such as frequency agility, adaptive

modulation, and transmit power control. These features allow the DSA devices to

1

communicate efficiently while minimizing the interference level to the legacy user

devices.

DSA radios need to determine the maximum possible power level that avoids the

harmful interference at the legacy user receivers. This power level is called Maximum

Interference Free Transmit Power (MIFTP) [2]. For a given transmit power, the path loss

is calculated using the propagation loss models and the interference level at the legacy

user receiver is estimated. Consequently, the accuracy of the path loss model used is very

important when determining the maximum power level of DSA transmitters such that

they will not interfere with the operation of licensed users.

There are two classes of propagation loss models: empirical models and

deterministic models. Empirical models are based on measured and averaged losses along

typical classes of radio links. Empirical Propagation Model (EPM-73) and Okumura –

Hata model are examples of empirical path loss models. Deterministic methods are based

on the physical laws of wave propagation and these methods produce more accurate and

reliable predictions of path loss compared to statistical methods. However, detailed and

accurate description of all objects in the propagation space is required for deterministic

methods; as a result, they are more expensive in computational effort. For instance,

Longley-Rice and TIREM path loss models are based on deterministic path loss models

combined with empirical measurements.

A novel path loss model called Location Based Propagation Modeling (LPM) is

presented in this thesis. The path loss models such as Longley-Rice and TIREM model in

the literature give the median loss value for a given distance between a transmitter and

2

receiver pair. The user needs to know the precise locations of the transmitter and receiver

to calculate the path loss with these models. However, the precise transmitter and/or

receiver locations are usually not known in spectrum sharing applications. Moreover,

TIREM and Longley-Rice models require detailed terrain information to calculate path

losses, but DSA devices have limited memory. These were the motivations to develop

LPM, which does not require precise locations of the transmitter and receiver. Moreover,

LPM does not require a lot of memory space to store the detailed terrain data.

In LPM, a given area is first divided into smaller sub-areas (called tiles), which

have similar terrain features. Then, the probability density functions of losses are

obtained for each tile by sampling loss values. By using tiles, the local terrain

characteristics are reflected more accurately than if a single pdf were used to represent

the entire coverage area. Furthermore, the location uncertainty problem is solved with the

tiling approach.

A survey of the well-known propagation models is provided and their advantages

and disadvantages are discussed in Chapter 2. The LPM model and tiling algorithm are

explained in Chapter 3. Application of LPM to opportunistic spectrum access is

explained in Chapter 4 and a performance evaluation of LPM is given in Chapter 5.

Spectrum sensing via the multitaper method is discussed in Chapter 6 and conclusions are

given in Chapter 7.

3

Chapter 2: Propagation Models

The power intensity of an electromagnetic wave reduces when it propagates

through space. This attenuation in power intensity is called path loss. Path loss may be

due to many effects, such as free space loss, refraction, diffraction, reflection, aperture-

medium coupling loss, and absorption [4]. A radio propagation model is a mathematical

formulation for the characterization of path loss as a function of frequency, distance and

other conditions. Different models have been developed to meet the needs of realizing the

propagation behavior in different conditions.

2.1 Empirical Propagation Model (EPM-73)

Empirical Propagation Model (EPM-73) is an empirical propagation model that

has the advantage of simplicity of manual calculations of basic transmission loss. In

many cases, detailed terrain data is not available and in some cases path loss calculations

are required for mobile devices. EPM-73 is a model that provides reasonably accurate

estimates of expected losses with minimal input information. Only antenna heights,

frequency and path-length information are required as the input parameters while

calculating the loss. For the frequency range of 20–100 MHz, the path loss predictions

from EPM-73 are as good as those produced using more complicated models [5].

4

2.2 Okumura - Hata Propagation Model

The Okumura – Hata model is the most widely used empirical propagation loss

model in radio frequency propagation to predict the behavior of cellular transmission in

urban areas that have a high building density. The input parameters for the model include

frequency, antenna height of base station, antenna height of mobile station and the

distance between the base station and the mobile station. The locations of the transmitter

and receiver are not required to calculate the loss in this model. The terrain size (small,

medium, large) and type (urban, suburban, open) are also specified by the user as input

parameters while calculating loss [6].

There are some restrictions while specifying input parameters of the Okumura -

Hata model. For instance, the input frequency must be between 150 MHz and 1000 MHz.

Moreover, the distance between the transmitter and receiver must be between 1 km and

20 km. As a result, the model is accurate only when the distance between the transmitter

and receiver is less than 20 km. The antenna height of the base station must be between

30 m and 200 m and the antenna height of the mobile station must be between 1 m and 10

m to obtain reasonable predictions.

As only four parameters are required for the Okumura-Hata model, the

computation time is short. This is an advantage of this model. However, the model

neglects the terrain profile between transmitter and receiver, i.e., hills or other obstacles

between the transmitter and the receiver are not considered. Phenomena like reflection

and shadowing are not included in the model, as well. Free space loss and diffraction by

the smooth earth are extensively treated while calculating the loss with this model.

5

2.3 Longley-Rice Propagation Model

The Longley – Rice propagation loss model is a general purpose model based on

electromagnetic theory and on statistical analyses of both terrain features and radio

measurements. It has been adopted as a standard by the FCC to evaluate TV service

coverage [7]. The model predicts the median transmission loss of a radio signal as a

function of distance and the variability of the signal in time and in space over irregular

terrain between 20 MHz and 10 GHz. The model uses free-space loss, diffraction by

smooth earth, reflection from earth surface, and atmospheric refractivity to give the

median value of losses.

The Longley – Rice path loss model has two parts: a model for predictions over

an area and a model for point-to-point link predictions. The point-to-point prediction

requires detailed terrain information. The set of parameters that must be defined to find a

particular path loss include frequency, polarization, path length, antenna heights above

ground, surface refractivity, effective earth’s radius, climate, ground conductivity, and

ground dielectric constant. Precise locations of transmitter and receiver are required for

this model. If a detailed terrain path profile is not available, the resulting prediction is

called ‘area’ mode prediction [8].

2.4 TIREM Propagation Model

Terrain Integrated Rough Earth Model (TIREM) predicts radio frequency

propagation loss over irregular terrain and seawater for ground-based and air-borne

transmitters and receivers [9]. The model is in the form of a computer program and a

6

digitized database of terrain elevations is required for the model. The inputs to the

program are frequency (40 MHz to 20 GHz), polarization, ground permittivity and

conductivity, atmospheric refractivity modulus, absolute humidity, and transmitter and

receiver antenna structural heights, site elevations, latitudes and longitudes. The program

gives the median path loss and fading statistics as outputs. The techniques used to

calculate the median loss are free space spreading, reflection, diffraction, surface-wave,

tropospheric-scatter, and atmospheric absorption. The model applies when either the

transmitter or the receiver is below 30,000 meters. The precise transmitter and receiver

locations are required by the model and the computation time is proportional to the

terrain resolution.

The path loss values obtained using TIREM and Longley-Rice model are very

close to each other. However, the TIREM model is usually the preferred path loss model

for tactical military radios for the Department of Defense.

7

Chapter 3: Location-Based Propagation Model (LPM)

TIREM path loss model is a complex propagation model and takes the latitude,

longitude and elevation data into account while calculating path loss values and gives the

median path loss value as output. This model requires detailed terrain information stored

in the memory in advance to calculate path loss. However, DSA devices have limited

memory and storing the terrain data for a very large region is not possible. A ‘compact’

path loss model which provides the same accuracy as a deterministic model and occupies

less memory is required.

Additionally, the user needs to know the precise locations of the transmitter and

receiver to calculate the path loss with TIREM model, but there is location uncertainty in

spectrum sharing applications. As a result, we have to take this uncertainty into account

to calculate MIFTP. We represent the location uncertainty in terms of probability density

function (pdf) of loss values for a given distance with LPM.

DSA radios are planned to be used in TV bands and the locations of TV

transmitters are known in advance, but the precise locations of the receivers are not

known. As a result, DSA devices have to be conservative while calculating MIFTP to

minimize the interference level at legacy user receiver. Figure 3.1 illustrates a scenario

where a DSA node transmitter causes interference to the legacy user receiver.

8

Figure 3.1 Interference Caused to the Legacy User Receiver.

The pdfs of loss values help DSA devices to determine MIFTP in case there is not

enough information about the locations of legacy user receivers. Low percentiles of pdf

of losses, i.e., 1st percentile, should be used to determine MIFTP if the terrain and

location information is not sufficient. In other words, by using pdf of losses, the user

knows how much conservative the DSA device needs to be in order not to affect the

operation of legacy users.

The memory requirement and location uncertainty in spectrum sharing

applications were the main motivations to obtain a new approach called Location-Based

Propagation Model (LPM), based on the existing TIREM model. LPM model uses a

tiling algorithm which is explained in detail in the next section.

9

3.1 Tiling Algorithm

LPM path loss model includes tiling algorithm. A given area is divided into sub-

areas according to some user defined criteria and the loss data for each sub-area is stored

in the memory for the tiling algorithm.

The path loss values are heavily dependent on the area where the transmitters and

receivers are located. Thus, the path loss can be very different between two transmitter

and receiver pairs in an urban and open area even though they have the same distance

between each other. Figure 3.1.1 is obtained using the real terrain data. The

measurements for the terrain data were taken in Virginia and Maryland in U.S. between

the latitudes of 38O and 40O, and the longitudes of -80O and -76O. For instance, if we

choose 2,000 uniformly distributed transmitter and receiver pairs with a fixed distance of

20 km between each other in the area shown in Figure 3.1.1 and calculate the path loss

values using TIREM path loss model, we obtain the non-parametric probability density

function of losses given in Figure 3.1.2. Normalized histograms are used to obtain the

non-parametric pdfs.

10

Figure 3.1.1 Terrain Profile.

110 120 130 140 150 160 1700

0.01

0.02

0.03

0.04

0.05

0.06

Loss Data (dB)

PD

F(us

ing

non-

para

met

ric fi

t)

Non-parametric pdf of losses for 2000 samples

Figure 3.1.2 Non-parametric pdf of Losses for the Whole Region.

11

Furthermore, if the region of interest is divided into smaller areas as in Figure

3.1.Figure 3.1.3, it can be seen that the non-parametric pdf of losses for the small areas

are quite different compared to the one for the whole region. The plots of non-parametric

pdfs of losses are given in Figure 3.1.4.

Figure 3.1.3 Coverage Area Divided into Sub-areas.

12

110 120 130 140 150 160 1700

0.01

0.02

0.03

0.04

0.05

0.06

Loss Data (dB)

PD

F(us

ing

non-

para

met

ric fi

t)

Non-parametric pdf of losses for 2000 samples

NP(A/64)NP(A/16)NP(A/4)NP(A)

Figure 3.1.4 Non-parametric pdf of Losses for Sub-areas.

As another example, when we divide the given region into quadrants as shown in

Figure 3.1.5, the non-parametric pdfs of losses are given in Figure 3.1.6. The pdf of

losses change significantly when the size of the area of interest is increased.

13

Figure 3.1.5 Whole Region Divided into Quadrants.

110 120 130 140 150 160 1700

0.02

0.04

0.06

0.08

0.1

0.12

Loss Data (dB)

PD

F (u

sing

non

-par

amet

ric fi

t)

Non-parametric pdf of losses for 2000 samples

NP(A)NP(A/4, quadrant#2)NP(A/4, quadrant#1)NP(A/4,quadrant#3)NP(A/4, quadrant#4)

Figure 3.1.6 Non-parametric pdf of Losses for Quadrants.

14

Consequently, since pdf of losses are calculated for the areas that have similar

terrain characteristics in the tiling approach, the resulting pdfs of losses reflect the terrain

features better.

The tiling algorithm divides a given area into sub-areas according to user defined

criteria and stores the mean and variance values of the probability loss distributions in the

memory for each distance bin in each tile. All the path loss calculations are done in

advance and the mean and the variance values for the loss distributions, which are output

parameters of tiling algorithm, are stored in the memory.

Suppose we approximately know the location of the DSA node transmitter, but

we don’t know the location of the legacy user receiver. Furthermore, we need to calculate

the path loss between the transmitter and receiver in order to determine the MIFTP. Since

we have some information about the location of the transmitter, we choose the tile that

covers this transmitter location and retrieve the path loss value from the memory for the

corresponding distance bin. In addition, the user can choose different percentiles of the

pdf of losses while obtaining the path loss. The chosen percentile value depends on the

application and the amount of information the user has for the approximate location of

the legacy user receiver. The probability of harmful interference to the legacy user

receiver decreases with this approach.

The user specifies the latitude, longitude and elevation data for the region of

interest, the minimum and maximum distance between the transmitter and receiver pairs,

the frequency range, the transmitter and receiver antenna heights and the polarization of

the antennas at the beginning of the program.

15

In tiling algorithm, first, initial seed size is specified (Figure 3.1.7). The initial

seed is a square with a seed length of max*2 d where is equal to the maximum

distance value that the user specifies as one of the input parameters. Once the initial seed

size is determined, a user-specified number of transmitter and receiver pairs are chosen in

the seed and the path losses are calculated for each of these pairs using TIREM path loss

model. If the user chooses a small number of transmitter and receiver pairs in the area,

then a different tiling will be obtained in each execution of the code since the chosen

samples will reflect different features of the terrain. On the other hand, if a very large

number of samples are chosen, then the time to compute the LPM model will be more.

The user should decide to the number of samples in the area depending on the

application.

maxd

After calculating the path losses between transmitters and receivers, the

probability density functions of the loss values are approximated using normal pdfs,

because the normal pdfs fit the distribution of losses better compared to other

distributions. The first percentile of the normal distribution is saved in the memory as the

variable L0 (Figure 3.1.8). Percentile value is also an input parameter for the model; as a

result, a user can choose some other percentile values instead of the first percentile.

16

Figure 3.1.7 Initial Seed.

Figure 3.1.8 First Percentile of Loss Distribution for the Initial Seed.

17

We start to increase the tile length diagonally after obtaining the initial seed. Each

time the area of the tile is increased, the number of transmitter and receiver pairs and the

maximum distance between the pairs are also increased. The losses between new

transmitter and receiver pairs are again calculated for the new area and the first percentile

of the new loss distribution is stored in the memory as the value L. Diagonal growth is

stopped if the difference between L and Lo is larger than a user specified value, €o. This

value is equal to 0.01 in our application. The diagonal increase of the tile size is

illustrated in Figure 3.1.9.

Figure 3.1.9 Diagonal Increase of the Seed Size.

When the difference between L and Lo turns out to be larger than €0, a diagonal binary

search is applied to find the optimum seed size (Figure Figure 3.1.10 – Figure 3.1.13).

The algorithm is named as diagonal binary search since we apply binary search

18

technique when the seed size is increased diagonally. It is assumed that the optimum

point is in the middle of the previous tile length and the current tile length when |L – L0| >

€0, thus all the calculations are repeated for the mean tile length while the difference

between L and Lo satisfies the initial criteria, i.e. |L – L0| ≤ €0.

Figure 3.1.10 Diagonal Binary Search – Mean Seed Length is Found.

19

Figure 3.1.11 Diagonal Binary Search – Check the Difference between L and Lo.

Figure 3.1.12 Diagonal Binary Search – Continue if the Initial Criteria is not Satisfied.

20

Figure 3.1.13 Diagonal Binary Search – Optimum Seed Size is Determined Diagonally.

The terrain features change dramatically when we keep increasing the area of the

seed diagonally at the end of diagonal binary search. At this point, we start to increase the

seed size horizontally. The seed keeps growing if the characteristic of the area does not

differ with fixed latitude and increasing longitude. Basically, we apply the same

procedure as we did in diagonal growth – continue to increase the area of the seed

horizontally as long as the initial criteria is satisfied such that |L - Lo| ≤ €o (Figure 3.1.14).

21

Figure 3.1.14 Horizontal Growth.

Horizontal binary search is applied when the difference between the first

percentile values for the previous seed and the current seed exceeds the pre-defined

value, €0, at the end of horizontal binary search (Figure 3.1.15).

22

Figure 3.1.15 Horizontal Binary Search.

The optimum longitude value for the sub-area is found at the end of the horizontal

binary search. We start to increase the latitude value of the seed at this point. As a result,

we start to enlarge the seed vertically by increasing the latitude. Figure 3.1.16 illustrates

the vertical growth of the seed.

23

Figure 3.1.16 Vertical Growth.

When the difference between the first percentile value of the previous seed and

the current seed is larger than the pre-specified value, €0, at the end of vertical growth, we

start to apply vertical binary search (Figure 3.1.17).

24

Figure 3.1.17 Vertical Binary Search.

The basic idea of vertical binary search is the same as diagonal and horizontal

binary search. The vertical growth stops when the optimum latitude value is found. At the

end of all these steps, the first sub-area which has similar terrain features is obtained. In

other words, if the tile length for this sub-area is increased further, the pdf of loss

distribution will differ dramatically compared to the initial seed.

Tiling the region is continued until the whole area of interest is covered with

small sub-areas. Figure 3.1.18 shows the area covered with tiles. Sub-areas do not

overlap in Figure 3.1.18 for illustration purposes, but in the real application, sub-areas

overlap while tiling the region (Figure 3.1.19). The distances between transmitters and

receivers are uniformly distributed between 40 km and 50 km and the transmit frequency

is uniformly distributed between 560 MHz and 600 MHz to obtain the tiling in Figure

25

3.1.19. The start and end points of all the tiles are saved in the memory after the whole

region is covered with tiles. The tile which covers a given transmitter or receiver location

is determined using saved start and end values of the sub-areas.

Figure 3.1.18 Tiled Region.

26

-80 -79.5 -79 -78.5 -78 -77.5 -77 -76.5 -7638

38.2

38.4

38.6

38.8

39

39.2

39.4

39.6

39.8

40TILED REGION dmin=40 km distmax=50 km, freqmin=560 MHz freqmax=600 MHz

Longitude (deg)

Latit

ude

(deg

)

Figure 3.1.19 Tiled Region with Overlapping Sub-areas.

27

Chapter 4: Application of LPM to Opportunistic Spectrum Access The application of LPM to opportunistic spectrum access is discussed in this

chapter.

4.1 Determining the Percentile of Loss for a Given Transmitter and Receiver

A given area is divided into sub-areas in tiling approach and each tile is assigned

a number as shown in Figure 4.1.1.

Figure 4.1.1 Numerated Tiles.

28

A sufficient number of transmitters and receivers proportional to the area size

have already been chosen while determining sub-areas in tiling algorithm. Moreover, the

corresponding path losses have been calculated. This information was required to obtain

the first percentile of pdf of losses, L and L0 values, during tiling algorithm. Using the

same transmitter and receiver locations, distances between transmitter and receivers can

be divided into distance bins with a user defined resolution and corresponding loss values

can be used to obtain pdf of losses for each distance bin in each tile.

Suppose the user has defined the distances between transmitters and receivers to

be uniformly distributed between minimum distance ( ) and maximum distance

( ) values for the initial seed of each tile in tiling approach. Maximum distance value

is increased during the execution of the code each time the area of the seed is increased

diagonally, horizontally or vertically. As a result, each tile has a different maximum

distance value at the end. For instance, since there are 23 tiles in the area given in Figure

4.1.1, we can represent each maximum distance value as where i represents the tile

number which is between 1 and 23. Suppose the user has also specified the distance bin

size as . The distances in the same distance bin will be grouped together and the

normal pdf of losses will be obtained by using the corresponding losses for each distance

value in the bin. In the end, we have number of distributions for every tile and

mind

maxd

id max

dΔ

in

dddnii Δ−= /)( minmax

where 1 ≤ i ≤ 23.

29

Table 4.1.1 shows grouping distances into bins for the ith tile.

Table 4.1.1 Grouping Distances into Distance Bins.

Distance Bin Pdf of Losses

ddd Δ+→ minmin )(1, xf i

dddd Δ+→Δ+ 2minmin )(2, xf i

dddd Δ+→Δ+ 32 minmin )(3, xf i

.

.

.

.

.

.

iddnd i maxmin )1( →Δ−+ )(3, xf i

Only the mean and the variance values need to be stored in the memory for each

normal distribution.

All the above calculations will be done and stored in the memory of DSA devices

in advance. As a result, there will not be any loss computation during the use of DSA

radios. The DSA nodes will only find the correct tile and corresponding distance bin in

the tile to find the mean and the variance value for the loss distribution for that distance

bin. As a result, computation time will be short to obtain the path loss. Moreover, with

this approach, we overcome the problem of occupying too much memory space while

storing detailed terrain information in the memory.

Obtaining the loss value is relatively easy when the transmitter and receiver are in

the same tile compared to the case when they are in different tiles. It is enough to take

into account the mean and the variance of the loss distribution from the tile that covers

30

transmitter and receiver when they are in the same tile. Suppose we know the

approximate location of a transmitter in an area. We want to calculate the path loss for an

approximate distance from the receiver with LPM when the transmitter and receiver are

in the same tile.

Figure 4.1.2 shows the case when the transmitter and receiver are in the same tile.

Figure 4.1.2 Transmitter and Receiver Pair in the Same Tile.

First, the tile which covers the given transmitter is found. For instance, the

transmitter and receiver are in the 8th tile (see Figure 4.1.1) in Figure 4.1.2. Then, the

distance bin which contains the distance between the transmitter and receiver is

determined in the corresponding tile. The mean and the variance of the loss distribution

for the given distance bin is retrieved from the memory. Then, the user can choose the

31

percentile value and obtain the path loss for that percentile. The value used as percentile

depends on the information the user has about the location of the transmitter and receiver.

Lower percentile values, i.e. 1st percentile, should be chosen to decrease the probability

of interference if the user does not have enough information about the locations.

Equation 4.1.1 gives the formula used to calculate the specified percentile of loss,

percentile, using the mean, μ , and variance, of the normal distribution. 2σ

Equation 4.1.1.

)100

(* percentileinvQL σμ −=

where dtexQx

t

∫∞

−

Π= 2

2

21)( .

On the other hand, if the transmitter and receiver pairs are in different tiles, the

mean and variance of the loss distribution is found considering the mean and variance of

the loss distribution from all the tiles between the given transmitter and receiver.

If the distance between a given transmitter and receiver is shown as d and each

portion of line d in different tiles is represented as di, then

Equation 4.1.2

ni ddddd +++++= ......21

32

where is the portion of the line between transmitter and receiver in the tile which

contains the transmitter, and is the portion of the line in the tile which contains the

receiver (Figure 4.1.3).

1d

nd

Figure 4.1.3 Transmitter and Receiver Pair in Different Tiles.

The sum of normal distributed variables has also a normal distribution. We use

this property of normal distribution when we combine loss data from different tiles when

the transmitter and receiver are in different tiles. If the mean and the variance of the

individual tiles are shown as μi and , respectively, when transmitter and receiver are in

different tiles the mean and variance of the distribution of losses are given by:

2iσ

33

Equation 4.1.3

( ) ( ) ( ) ( ) nnii dddddddd μμμμμ */...*/...*/*/ 2211 +++++=

( ) ( ) ( ) ( ) 222222

22

21

21

2 */...*/...*/*/ nnii dddddddd σσσσσ +++++=

The specified percentile of loss is again calculated using Equation 4.1.1 with the

mean and variance values obtained in Equation 4.1.3.

4.2 Using LPM to Determine MIFTP

Maximum Interference Free Transmit Power (MIFTP) is the maximum transmit

power level a DSA device can use without causing harmful interference to the legacy

user receivers. The LPM approach is very useful when determining the MIFTP for a DSA

device since one can determine a path loss value without using the exact locations of

transmitter and receiver. The interference range for legacy user receivers can be

calculated and the transmit power level of the DSA devices can be adjusted using this

path loss value.

The pdf of losses for the untiled region can be used when there is no information

about either the location of the transmitter or the receiver. Choosing lower percentiles of

pdf of losses will be more appropriate in this case. For the cases when we at least know

the approximate location of either the transmitter or receiver, we can use the pdf of losses

for the tiled region by retrieving the loss data from the appropriate tiles. If there are lots

of obstacles which will cause absorption in the area, higher percentile losses can be used

(i.e., 10%), but if the transmitters and receivers are in an open area, then the path loss will

be small and the received signal level at the non-cooperative node receiver will be high.

34

Thus, it will be more appropriate to use lower percentiles of loss distributions (i.e., 1%)

in an open area.

35

Chapter 5: Performance Evaluation of LPM

Three criteria are considered to evaluate the performance of the LPM path loss

model: memory requirement, violation probability and calculation time.

5.1 Memory Requirement

Probability density functions of losses are obtained for every distance bin in each

tile while using LPM. Thus, the number of pdf of losses saved for each tile differs

depending on the resolution chosen while grouping the distances. The number of pdf of

losses saved also depends on the number of tiles in the area. If the terrain characteristics

differ dramatically in the given area, the number of tiles and the amount of data to be

saved will increase. For instance, DSA devices are planned to be used all over the U.S.;

as a result, the data for the map of whole country would have to be saved in the memory

of each DSA device for each tile. The required memory with LPM would be very large in

this case. We tried to overcome this problem by converting the non-parametric

distribution of losses to normal distribution and saving only the mean and the variance in

the memory for each distance bin in each tile.

While generating the LPM path loss model, we worked with a relatively small

area, with a size of 222 km x 350 km. There are 23 tiles in the tiled region in Figure

4.1.1, and the required memory to save the parameters of normal distribution and start

36

and end points for all the tiles and input parameters are 96 kbytes. However, the required

memory space to store the terrain data with TIREM model for the same area is 1.38

Mbytes. As a result, LPM model requires very small memory space compared to TIREM

model. Moreover, the memory requirement can be decreased further in LPM by

increasing the resolution of the distance bins and the size of each tile depending on the

application by adjusting the €0 value, i.e. stop increasing the area of the tile when |L – L0|

> €0 = 0.1 instead of |L – L0| > €0 = 0.01.

5.2 Violation Probability

One other criteria considered while evaluating LPM is violation probability. The

path loss values from TIREM model are accepted as truth and ‘violation’ is defined as the

time the first percentile of the pdf of losses from LPM model exceed the loss value

obtained using the TIREM model, i.e. LLPM > LTIREM. The results from both untiled and

tiled regions are considered while calculating the violation probability and the results are

given in this section.

For the untiled region, the violation probability is 0.04% for 2500 samples. On the

other hand, violation probability is 0.72% for 2500 samples for tiled region. LPM loss

value is 2 or 3 dB higher than the one for TIREM model for most of the violation cases.

The mean of the difference between TIREM model path loss and LPM path loss is

( ) dB with a 95% confidence level. As a result, violation probability is less

than 1% with LPM and the impact of the interference will not be very high compared to

01.03.48 ±

37

TIREM model even in the case of interference since there is not a big difference between

path loss values when violation occurs.

5.3 Calculation Time

TIREM model takes the locations of transmitter and receiver and detailed terrain

data as input parameters and gives the path loss value as output. On the other hand, all the

loss calculations are done in advance with LPM and the mean and variance values of the

loss distributions of each distance bin in each tile are saved in the memory. In other

words, instead of calculating path loss, LPM model retrieves the path loss data from the

memory. As a result, it is expected that LPM model takes less time compared to TIREM

model.

The number of tiles between the transmitter and receiver affects the calculation

time for LPM. For instance, in Figure 5.3.1, several tiles has to be gone through and

mean and variance of the loss distribution in those tiles for the corresponding distance

bins has to be considered in order to find the final path loss with LPM. On the other hand,

checking the loss distribution of only one tile is enough for Figure 5.3.2 since the

transmitter and receiver are in the same tile.

38

Figure 5.3.1 A Given Transmitter and Receiver Far Away From Each Other.

Figure 5.3.2 A Given Transmitter and Receiver Close to Each Other.

39

MATLAB is used for LPM, and TIREM model is written in the C language.

Moreover, some ‘for’ loops have to be used in MATLAB code while calculating path

losses with LPM. As a result, this increases the calculation time for LPM and it is not a

fair comparison to compare the execution time for TIREM and LPM in two different

programming environments. However, since path loss calculations are done in advance

with LPM model, the TIREM model should take more time compared to LPM if they

were implemented using the same programming language.

40

Chapter 6: Spectrum Sensing via the Multitaper Method

A new approach to determine the MIFTP more accurately is explained in Chapter

3 through Chapter 5. However, DSA devices need to sense the channel and determine

that the signal level is below a threshold value at that frequency in a certain time and

location before starting to use the channel and determining MIFTP.

A spectrum hole can be defined as a frequency band that is not being used by a

primary user at a particular time and geographic region [10] and as mentioned before,

spectrum sharing can be performed by DSA nodes, which have the capability of

dynamically tuning to spectrum holes within a frequency range. To determine the

spectrum holes accurately, a DSA node should be equipped with a highly sensitive

detector and an algorithm to access the unused spectrum without causing harmful

interference to the primary users of the spectrum. In this section, the multitaper (MT)

spectral estimation method is applied to the problem of spectrum sensing in TV bands

and the performance of the MT method is compared with that of conventional FFT-based

spectrum estimation [11].

41

6.1 Spectral Estimation

Spectrum holes are determined by examining the power spectral density of the

received signal. Therefore, accurate and efficient methods of power spectral estimation

are required to determine the spectrum holes.

In [12], ultra-sensitive TV detector measurements are analyzed using the

conventional FFT-based method. The MT method was introduced by Thomson [13] and

has been shown to have superior performance in some applications such as geoclimate

sensing [14]. Haykin [1] suggests that the multitaper method would be effective in

spectrum sharing applications, but we are not aware of empirical studies applying the

multitaper method to spectrum hole detection using real measurement data. In [12], the

conventional FFT method is used to study TV detector measurement data. In this chapter,

we compare the performance of the FFT method versus the MT method with respect to

spectrum sensing using the empirical TV measurement data from [12].

6.1.1 Conventional FFT Method

Given a time series, , the conventional FFT method estimates the

power spectral density as follows:

},...,,{ 21 NXXX

( ).S

Equation 6.1.1

( )2

1

2∑=

Δ−Δ Δ=

N

t

tftjt

fft eXNtfS π ,

42

where is the spacing between the samples. The function is known as the

periodogram [15]. The periodogram is an unbiased estimate of the power spectral density

for white Gaussian noise, but its variance is equal to a constant that is independent of the

data length . As a result, as . Hence, the periodogram is an

inconsistent estimator of the power spectrum [15].

tΔ )( fS fft

N 0)]([ ≠fSVar fft ∞→N

6.1.2 Multitaper Method

Multitaper spectral analysis is a method for spectral estimation of a time series

that is believed to exhibit a spectrum containing both continuous and singular

components. This method involves the use of a set of K orthogonal tapers, called

Discrete Prolate Spheroidal Sequence (DPSS) tapers. K represents the tradeoff between

resolution and the variance properties of the spectral estimate. The variance of the

spectral estimate can be decreased when K is large. On the other hand, we smear out the

fine features and decrease the resolution of the spectral estimate by increasing the value

of K . The taper is a sequence . Each taper provides protection

against spectral leakage [13]. The time series data is windowed with each of the

thk },...,1,0:{ , Nth kt =

K DPSS

tapers and then a periodogram is computed via the FFT [15]. The high resolution

multitaper spectrum is a weighted sum of K eigenspectra, (see

[16], p. 369):

1,...,0(.),^

−= KkS mtk

43

Equation 6.1.2

∑

∑−

=

−

=

∧

Δ= 1

0

1

0

)()( K

kk

K

k

mt

kkmt

fSfS

λ

λ ,

where

2

1

2,)( ∑

=

Δ−Δ∧

Δ=N

t

tftjtkt

mt

k eXhtfS π ,

kth , is the DPSS taper element for the direct spectral estimator , and tht thk (.)mt

kS∧

kλ is

the eigenvalue corresponding to the eigenvector with elements (see [16], p. 103). }{ ,kth

A more leakage-resistant spectral estimate, called an adaptively weighted

multitaper (AWMT) spectrum, can be obtained by adjusting the relative weights on the

contributions from each of the K eigenspectra as follows (see [16], p. 370):

Equation 6.1.3

∑

∑−

=

−

=

∧

Δ= 1

0

2

1

0

2

)(

)()()( K

kkk

K

k

mt

kkkamt

fb

fSfbfS

λ

λ

where is a weighting function that further guards against broadband leakage for a

non-white (“colored”) but locally-white process. The weight of the eigenspectrum is

proportional to , where

)( fbk

thk

kk fb λ)(2

44

tfSfSfb

kkk Δ−+

= 2)1()()()(

σλλ.

Parseval’s theorem is satisfied in expected value in Equation 6.1.2, because the

weights in the estimator do not depend on the frequency. On the other hand, the AWMT

spectral estimator given in Equation 6.1.3 generally does not satisfy Parseval’s theorem

in expected value [16].

6.2 Numerical Results

Spectrum measurements were made at a residential location in McLean,

Virginia1. The equipment was connected to a standard TV antenna located on the second

story roof. The measurement data consists of time series data collected over a period of

approximately 8 minutes for 40 different starting times. Thus, we have a collection of

sets of time series data available to us, which we represent by , where

denotes the sample in the data set with and where

. The time spacing between samples is ms.

40=M }{ )(itX

)(itX tht thi Mi ,...,1= ,,...,1 Nt =

200,819=N 586.0=Δt

Figure 6.2.1 and Figure 6.2.2 show three types of graphs corresponding to the

FFT and MT methods, respectively:

a) maximum hold (max-hold) plot,

b) waterfall plot,

c) duty cycle plot.

1 The measurements were taken by Shared Spectrum Company.

45

Figure 6.2.1 Max-Hold Plot for TV Channel 3 Using the FFT Method.

Figure 6.2.2 Max-Hold Plot for TV Channel 3 Using the MT Method.

46

Both the standard MT and the AWMT methods are applied to the data and no

significant difference is observed in the results. The results presented in this thesis are

obtained using AWMT method with K = 7 tapers.

Let denote the spectral estimate obtained from the first

samples of the data set or time series (using the FFT method or the MT method). The

max-hold power spectral estimate is defined by

)( fSi 000,18=N

thi

Equation 6.2.1

),(max)(1

fSfS iMimh ≤≤

Δ= ,hl fff ≤≤

where MHz and MHz. The waterfall plot shows the set of points

for which the spectral estimate exceeds a given threshold

2.61=lf 3.61=hf

),,( if )( fSi η over the M

data sets. The set of points in the waterfall plot can be expressed as

Equation 6.2.2

}.,1,)(:),{( hli fffMifSifW ≤≤≤≤≥=Δ

η

The duty cycle plot shows, for each frequency the proportion of data sets for

which exceeds the threshold

,f

)( fSi η . In other words, the value of the duty cycle plot at

the frequency value is given by f

47

Equation 6.2.3

,11)(1

})({∑=

≥

Δ=

M

ifsiM

fd η ,hl fff ≤≤

where denotes the indicator function on the set Thus, the duty cycle plot renders

negligible spectral components that have high power for only a small number of data sets.

A1 .A

For the waterfall and duty cycle plots in Figure 6.2.1 and Figure 6.2.2, detector

threshold values of 110−=η dBm and 119−=η dBm were used, respectively.

Comparing these two figures, we can make the following qualitative observations. From

the maxhold plots, we see a smaller variation in the spectral estimates obtained via the

MT method. The average signal level in the max-hold plot is lower in the case of the MT

method, since it is able to suppress more of the noise components. From the waterfall

plots, we see that the MT method removes misleading information. From the duty cycle

plots obtained using the MT method, we can much more easily identify the carrier signal

and the synchronization pulses, which are 15 kHz apart from each other in each channel.

The duty cycle plots can be used to determine whether a channel is free or occupied at a

specific time.

The performance curves shown in Figure 6.2.3 through Figure 6.2.6 were

obtained using duty cycle plots for which the detector threshold value η was varied from

−120 to 0 dBm. To obtain these figures, power spectrum estimates corresponding to each

of the data sets were computed using the first samples from each set.

Note that this number of samples corresponds to a time period of approximately 35

40=M 1500=N

48

seconds. Then duty cycle values are computed using Equation 6.2.3 for a given value of

η .

Figure 6.2.3 shows the number of correctly identified busy channels versus the

threshold level for both the FFT method and the MT method. A channel is identified as

busy (i.e., a signal is present) if the duty cycle value corresponding to the carrier

frequency exceeds a threshold of 0.2 (i.e., 20%). Using a threshold value of 0.2 provides

an adequate probability of detection and probability of false alarm. In the MT method, the

noise components of the signal and the variance of the spectral estimate are reduced such

that the power of the MT-based estimate is less than that of the FFT-based estimate. As a

result, the number of detected channels is higher for the FFT method when the threshold

level is between -70 dB and -30 dB. However, in practice, such high values would not be

used as a detector threshold; opportunistic spectrum access requires much lower detector

thresholds. The objective here is to decrease the threshold as much as possible in order to

obtain accurate information about spectrum occupancy.

)( fd

49

Figure 6.2.3 Number of correctly identified busy channels vs. Threshold Value.

Figure 6.2.4 shows the number of false alarm channels versus the detector

threshold level. A false alarm channel refers to a channel that is identified as busy, when

it is actually free. We observe that the number of false alarm channels is lower for the

MT method when the threshold level is between -120 and -80 dBm.

50

Figure 6.2.4 Number of False Alarm Channels vs. Threshold Value.

Figure 6.2.5 shows the number of miss-detected channels versus the detector

threshold. A miss-detected channel refers to a channel that is identified as free, when it is

actually busy. The number of miss-detected channels is the same for both MT and FFT

methods for the threshold levels of interest.

51

Figure 6.2.5 Number of Miss-Detected Channels vs. Threshold Value.

Figure 6.2.6 shows the number of correctly identified free channels versus the

detector threshold. The correctly identified free channels represent the channels that are

available for spectrum sharing. The number of correctly identified free channels is higher

with MT method between -120 and -80 dBm. If we set a fixed threshold level, e.g. -100

dB and examine the statistics using this threshold level, we can see that the number of

correctly identified busy channels and the number of miss-detected channels are the same

for both methods. On the other hand, the number of false alarm channels is lower and the

number of correctly identified free channels is higher for the MT method. Thus, we see

that more channels can be harvested by means of the MT method compared with the FFT

method, using a lower threshold level.

52

Figure 6.2.6 Number of Correctly Identified Free Channels vs. Threshold Value.

53

Chapter 7: Conclusion

A novel path loss model, Location Based Propagation Modeling, based on the

existing TIREM model is developed in this thesis. The model divides a given region into

sub-areas based on user defined criteria and gives the probability density functions of

path losses for different distance bins in each sub-area. Only the mean and the variance of

losses are saved in the memory after obtaining the pdfs of losses. As a result, detailed

terrain information does not need to be saved in the memory to calculate the path losses.

Moreover, LPM does not require precise locations of transmitter and receiver as input

parameters. This feature of LPM makes it very useful for spectrum sharing applications.

The memory requirement, computation time and violation probability are

considered in evaluating the performance of the LPM path loss model. The memory

requirement for LPM is less compared to the TIREM model since all the path loss

calculations are done in advance and the mean and variance of pdf of losses are saved in

the database. The amount of data to be saved depends on the number of tiles and number

of distance bins in each tile since there is a loss distribution for each tile. For instance,

when the region of interest gets bigger, it is highly probable that the difference between

the terrain characteristics will increase. Thus, the number of tiles will increase. The LPM

model overcomes the memory problem by saving only the mean and the variance values

for distribution of losses for every distance bin in each tile.

54

The violation probability is given for both tiled and untiled regions in Chapter 5.

The violation probability is less than 1% and the path loss values are only 2 or 3 dB

higher than the loss from TIREM model in the violation cases.

It is expected that LPM model will be faster compared to TIREM model since all

the path loss calculations are completed offline and the data is stored in the memory in

LPM. With LPM, time is required to retrieve the data from the memory other than

calculating the path losses from the beginning. The code for LPM was written using

MATLAB and C language is used for TIREM model. As a result, it is not a fair

comparison to compare the calculation time for LPM and TIREM models using

MATLAB.

When the number of transmitter and receiver pairs chosen is not sufficient for the

initial seed, the size of tiles changes in every execution of the code for a given area. A

large number of samples should be used for each tile for the tiling to be consistent in

different executions of the code. In other words, we should be able to obtain the same

tiling for a given area regardless of the number of samples chosen. This will increase the

memory requirement, but give more stable results in the mean time. A database with

enough number of samples in each tile will be formed for bigger areas in ongoing work.

We mostly concentrated on determining MIFTP in this thesis, but localization is

also an important problem in spectrum sharing applications. The aim is to determine the

location of a receiver for a given transmit power and distance with localization. The path

loss model used is again very important in localization problem especially if the DSA

device uses a high transmit power.

55

The application of the multitaper method of spectral estimation to the problem of

spectrum harvesting in TV bands is also discussed in this thesis. It is known that the

computational complexity of the MT method is greater than that of the FFT method by a

factor of K, where K is the number of tapers used. However, for relatively small time

series, e.g., 1500 samples taken over 40 different data sets amounts to about 35 seconds,

the MT method is fast enough to be used in real-time. The performance of spectrum

harvesting using the conventional FFT method versus the MT method is compared using

empirical TV measurement data and the noise reduction properties of the MT method

relative to the FFT method are observed qualitatively from the max-hold, waterfall, and

duty cycle plots. The preliminary results with TV measurement data indicate that the

noise reduction property of the MT method can result in a significant gain in the number

of correctly identified free channels compared to the FFT method. This suggests that

significant gains in spectrum harvesting may be achievable in more general settings. In

ongoing work, the MT method will be applied to larger sets of measurement data from a

variety of signal sources.

56

BIBLIOGRAPHY

57

BIBLIOGRAPHY

[1] S. Haykin, “Cognitive Radio: Brain-Empowered Wireless Communications,” IEEE J. Selected Areas in Comm., vol. 23, pp. 201–220, Feb. 2005. [2] A. E. Leu, M. McHenry, and B. L. Mark, “Modeling and analysis of interference in listen-before-talk spectrum access schemes,” Int. J. Network Mgmt, vol. 16, pp. 131–147, 2006. [3] Zhu Ji, K. J. Ray Liu, “Dynamic Spectrum Sharing: A Game Theoretical Overview,” in IEEE Communications Magazine, May 2007. [4] Mohammad Ghavami, L. B. Michael, Ryuji Kohno, “Ultra Wideband Signals and Systems in Communication Engineering,” John Wiley & Sons, January 2005. [5] M.N. Lustgarten, James A. Madison, “An Empirical Propagation Model (EPM - 73),” in IEEE Transactions on Electromagnetic Compatibility, Vol. EMC-19, No. 3, August 1977. [6] Jon W. Mark, Weihua Zhuang, “Wireless Communications and Networking,” Prentice Hall, 2003. [7] Federal Communications Commission, www.fcc.gov/Bureaus/Engineering-Technology/Documents/bulletins/oet69/oet69.pdf [8] IEEE Vehicular Technology Society Committee on Radio Propagation, “Coverage Prediction for Mobile Radio Systems Operating in the 800/900 MHz Frequency Range,” in IEEE Transactions on Vehicular Technology, Vol. 31, No. 1, February 1988. [9] Alion Science and Technology Corporation, http://www.alionscience.com. [10] P. Kolodzy, “Next generation communications: Kickoff meeting,” in Proc. DARPA, October 2001. [11] T. Erpek, A. E. Leu, and B. L. Mark, “Spectrum Sensing Performance in TV Bands Using the Multitaper Method,” IEEE 15th Signal Processing and Communications Applications, 2007.

58

[12] A. E. Leu, K. Steadman, M. McHenry, and J. Bates, “Ultra Sensitive TV Detector Measurements,” in Proc. IEEE Int. Symp. on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), pp. 30–36, Nov. 2005. [13] D. J. Thomson, “Spectrum Estimation and Harmonic Analysis,” Proc. IEEE, vol. 70, pp. 1055–1096, September 1982. [14] M. E. Mann and J. Park, “Oscillatory spatiotemporal signal detection in climate studies: A multiple-taper spectral domain approach,” Advances in Geophysics, vol. 41, pp. 1–131, 1999. [15] T. P. Bronez, “On the Performance Advantage of Multitaper Spectral Analysis,” IEEE Trans. on Signal Proc., vol. 40, pp. 2941–2946, December 1992. [16] D. B. Percival and A. T. Walden, “Spectral Analysis for Physical Applications,” Cambridge University Press, 1993.

59

CURRICULUM VITAE

Tugba Erpek received the B.S. degree in Electrical Engineering from Osmangazi University, Eskisehir, Turkey, in 2005. She was a research assistant at Network Architecture and Performance Laboratory (NAPL) at George Mason University from 2005 to 2007. She is currently working at Shared Spectrum Company as a Systems Engineer. Her research interests include wireless communications and digital signal processing.

60